Relevant bibliographies by topics / Group theory

Academic literature on the topic 'Group theory'

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Published: 4 June 2021
Last updated: 28 July 2024

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Journal articles on the topic "Group theory"

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Berestovskii, Valera, and Conrad Plaut. "Covering group theory for compact groups." Journal of Pure and Applied Algebra 161, no. 3 (July 2001): 255–67. http://dx.doi.org/10.1016/s0022-4049(00)00105-5.

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Berestovskii, Valera, and Conrad Plaut. "Covering group theory for topological groups." Topology and its Applications 114, no. 2 (July 2001): 141–86. http://dx.doi.org/10.1016/s0166-8641(00)00031-6.

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BROWN, F., and N. G. MAROUDAS. "Group theory." Nature 348, no. 6303 (December 1990): 669. http://dx.doi.org/10.1038/348669b0.

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Porter, T. "Undergraduate Projects in Group Theory: Automorphism Groups." Irish Mathematical Society Bulletin 0016 (1986): 69–72. http://dx.doi.org/10.33232/bims.0016.69.72.

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Gordon, Gary. "USING WALLPAPER GROUPS TO MOTIVATE GROUP THEORY." PRIMUS 6, no. 4 (January 1996): 355–65. http://dx.doi.org/10.1080/10511979608965838.

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Berestovskii, Valera, and Conrad Plaut. "Covering group theory for locally compact groups." Topology and its Applications 114, no. 2 (July 2001): 187–99. http://dx.doi.org/10.1016/s0166-8641(00)00032-8.

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Xue, Zeqi. "Group Theory and Ring Theory." Journal of Physics: Conference Series 2386, no. 1 (December 1, 2022): 012024. http://dx.doi.org/10.1088/1742-6596/2386/1/012024.

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Abstract Group theory is an important theory in abstract algebra. A ring is a kind of algebraic system with two operations (addition and multiplication). It has a deep relationship with groups, especially with the Abelian group. In this essay, the ring and the residual class ring will be talked about. Firstly, this passage is aim to talk about some basic knowledge about the ring which will let readers have a basic understanding of a ring. Then this passage will discuss the residual class ring and subring of the residual class ring of modulo. Some concepts about the ring are also mentioned, such as the centre of the ring, the identity of the ring, the classification of a ring, the residual class ring, the field and the zero divisors. The definitions of mathematical terms mentioned before are stated, as well as some examples of the part of those terms are given. In this passage, there are also some lemmas which are the properties of ring and subring. Future studies of rings and subrings can focus on the application of physics.
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Wang, Mingshen. "Group Theory in Number Theory." Theoretical and Natural Science 5, no. 1 (May 25, 2023): 9–13. http://dx.doi.org/10.54254/2753-8818/5/20230254.

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The theory of groups exists in many fields of mathematics and has made a great impact on many fields of mathematics. In this article, this paper first introduces the history of group theory and elementary number theory, and then lists the definitions of group, ring, field and the most basic prime and integer and divisor in number theory that need to be used in this article. Then from the definitions, step by step, Euler's theorem, Bzout's lemma, Wilson's theorem and Fermat's Little theorem in elementary number theory are proved by means of definitions of group theory, cyclic groups, and even polynomials over domains. Finally, some concluding remarks are made. Many number theory theorems can be proved directly by the method of group theory without the action of tricks in number theory. Number theory is the thinking of certain special groups (e.g., (Z,+),(Z,)), so the methods of group theory work well inside number theory.
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Virginia Brabender. "Chaos Theory and Group Psychotherapy 15 Years Later." Group 40, no. 1 (2016): 9. http://dx.doi.org/10.13186/group.40.1.0009.

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Denton, Brian, and Michael Aschbacher. "Finite Group Theory." Mathematical Gazette 85, no. 504 (November 2001): 546. http://dx.doi.org/10.2307/3621802.

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Dissertations / Theses on the topic "Group theory"

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Isenrich, Claudio Llosa. "Kähler groups and Geometric Group Theory." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:4a7ab097-4de5-4b72-8fd6-41ff8861ffae.

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In this thesis we study Kähler groups and their connections to Geometric Group Theory. This work presents substantial progress on three central questions in the field: (1) Which subgroups of direct products of surface groups are Kähler? (2) Which Kähler groups admit a classifying space with finite (n-1)-skeleton but no classifying space with finitely many n-cells? (3) Is it possible to give explicit finite presentations for any of the groups constructed in response to Question 2? Question 1 was raised by Delzant and Gromov. Question 2 is intimately related to Question 1: the non-trivial examples of Kähler subgroups of direct products of surface groups never admit a classifying space with finite skeleton. The only known source of non-trivial examples for Questions 1 and 2 are fundamental groups of fibres of holomorphic maps from a direct product of closed surfaces onto an elliptic curve; the first such construction is due to Dimca, Papadima and Suciu. Question 3 was posed by Suciu in the context of these examples. In this thesis we: provide the first constraints on Kähler subdirect products of surface groups (Theorem 7.3.1); develop new construction methods for Kähler groups from maps onto higher-dimensional complex tori (Section 6.1); apply these methods to obtain irreducible examples of Kähler subgroups of direct products of surface groups which arise from maps onto higher-dimensional tori and use them to show that our conditions in Theorem 7.3.1 are minimal (Theorem A); apply our construction methods to produce irreducible examples of Kähler groups that (i) have a classifying space with finite (n-1)-skeleton but no classifying space with finite n-skeleton and (ii) do not have a subgroup of finite index which embeds in a direct product of surface groups (Theorem 8.3.1); provide a new proof of Biswas, Mj and Pancholi's generalisation of Dimca, Papadima and Suciu's construction to more general maps onto elliptic curves (Theorem 4.3.2) and introduce invariants that distinguish many of the groups obtained from this construction (Theorem 4.6.2); and, construct explicit finite presentations for Dimca, Papadima and Suciu's groups thereby answering Question 3 (Theorem 5.4.4)).
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Griffin, Cornelius John. "Subgroups of infinite groups : interactions between group theory and number theory." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252018.

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Coutts, Hannah Jane. "Topics in computational group theory : primitive permutation groups and matrix group normalisers." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2561.

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Part I of this thesis presents methods for finding the primitive permutation groups of degree d, where 2500 ≤ d < 4096, using the O'Nan-Scott Theorem and Aschbacher's theorem. Tables of the groups G are given for each O'Nan-Scott class. For the non-affine groups, additional information is given: the degree d of G, the shape of a stabiliser in G of the primitive action, the shape of the normaliser N in S[subscript(d)] of G and the rank of N. Part II presents a new algorithm NormaliserGL for computing the normaliser in GL[subscript(n)](q) of a group G ≤ GL[subscript(n)](q). The algorithm is implemented in the computational algebra system MAGMA and employs Aschbacher's theorem to break the problem into several cases. The attached CD contains the code for the algorithm as well as several test cases which demonstrate the improvement over MAGMA's existing algorithm.
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Martin, Michael Patrick McAlarnen. "Computational Group Theory." Thesis, The University of Arizona, 2015. http://hdl.handle.net/10150/579297.

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The study of finite groups has been the subject of much research, with substantial success in the 20th century, in part due to the development of representation theory. Representation theory allows groups to be studied using the well-understood properties of linear algebra, however it requires the researcher to supply a representation of the group. One way to produce representations of groups is to take a representation of a subgroup and use it to induce a representation. We focus on the finite simple groups because they are the buliding blocks of an arbitrary simple group. This thesis investigates an algorithm to induce representations of large finite simple groups from a representation of a subgroup.
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Garotta, Odile. "Suites presque scindées d'algèbres intérieures et algèbres intérieures des suites presque scindées." Paris 7, 1988. http://www.theses.fr/1988PA077184.

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Dans le cadre de l'etude des representations modulaires d'un groupe fini sur un corps, nous generalisons la notion, introduite par auslander et reiten, de "suite exacte presque scindee" de nodules (sur l'algebre de groupe), en une notion de "systemes d'idempotents" (dits systemes de auslander-reiten) dans une algebre "interieure" (du point de vue de l'operation du groupe) symetrique quelconque. Raisonnant a l'interieur des algebres, nous donnons, comme dans la theorie classique, un resultat d'"existence et unicite" des systemes de auslander-reiten. D'autre part le point de vue de l'"algebre commutante" des systemes nous permet de decrire, par le biais des groupes pointes, la restriction des systemes de auslander-reiten au vortex de leur terme extreme, et de donner un critere pour que ce vortex coincide avec celui du systeme. En particulier on a egalite pour les suites presque scindees se terminant par un module simple
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McSorley, J. P. "Topics in group theory." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376929.

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Hegedüs, Pál. "Topics in group theory." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620412.

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Colletti, Bruce William. "Group theory and metaheuristics /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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Menezes, Nina E. "Random generation and chief length of finite groups." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3578.

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Part I of this thesis studies P[subscript(G)](d), the probability of generating a nonabelian simple group G with d randomly chosen elements, and extends this idea to consider the conditional probability P[subscript(G,Soc(G))](d), the probability of generating an almost simple group G by d randomly chosen elements, given that they project onto a generating set of G/Soc(G). In particular we show that for a 2-generated almost simple group, P[subscript(G,Soc(G))](2) 53≥90, with equality if and only if G = A₆ or S₆. Furthermore P[subscript(G,Soc(G))](2) 9≥10 except for 30 almost simple groups G, and we specify this list and provide exact values for P[subscript(G,Soc(G))](2) in these cases. We conclude Part I by showing that for all almost simple groups P[subscript(G,Soc(G))](3)≥139/150. In Part II we consider a related notion. Given a probability ε, we wish to determine d[superscript(ε)] (G), the number of random elements needed to generate a finite group G with failure probabilty at most ε. A generalisation of a result of Lubotzky bounds d[superscript(ε)](G) in terms of l(G), the chief length of G, and d(G), the minimal number of generators needed to generate G. We obtain bounds on the chief length of permutation groups in terms of the degree n, and bounds on the chief length of completely reducible matrix groups in terms of the dimension and field size. Combining these with existing bounds on d(G), we obtain bounds on d[superscript(ε)] (G) for permutation groups and completely reducible matrix groups.
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Cornwell, Christopher R. "On the Combinatorics of Certain Garside Semigroups." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1381.pdf.

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Books on the topic "Group theory"

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Kegel, Otto H., Federico Menegazzo, and Giovanni Zacher, eds. Group Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078683.

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Hampton, Donna Jayne. Group theory. Oxford: Oxford Brookes University, 1999.

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Khattar, Dinesh, and Neha Agrawal. Group Theory. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-21307-6.

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Fine, Benjamin, Anthony M. Gaglione, and Dennis Spellman, eds. Combinatorial Group Theory, Discrete Groups, and Number Theory. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/conm/421.

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Kappe, Luise-Charlotte, Arturo Magidin, and Robert Fitzgerald Morse, eds. Computational Group Theory and the Theory of Groups. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/470.

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Bestvina, Mladen, Michah Sageev, and Karen Vogtmann. Geometric group theory. Providence, RI: American Mathematical Society, 2014.

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Kappe, Luise-Charlotte, Arturo Magidin, and Robert Fitzgerald Morse, eds. Computational Group Theory and the Theory of Groups, II. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/conm/511.

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Fuchs, László, Rüdiger Göbel, and Phillip Schultz, eds. Abelian Group Theory. Providence, Rhode Island: American Mathematical Society, 1989. http://dx.doi.org/10.1090/conm/087.

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Fine, Benjamin, Anthony Gaglione, and Francis C. Y. Tang, eds. Combinatorial Group Theory. Providence, Rhode Island: American Mathematical Society, 1990. http://dx.doi.org/10.1090/conm/109.

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Charney, Ruth, Michael Davis, and Michael Shapiro, eds. Geometric Group Theory. Berlin, New York: DE GRUYTER, 1995. http://dx.doi.org/10.1515/9783110810820.

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Book chapters on the topic "Group theory"

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Martínez-Guerra, Rafael, Oscar Martínez-Fuentes, and Juan Javier Montesinos-García. "Group Theory." In Algebraic and Differential Methods for Nonlinear Control Theory, 19–30. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12025-2_2.

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Mahan, Gerald Dennis. "Group Theory." In Applied Mathematics, 47–71. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-1315-5_3.

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Stillwell, John. "Group Theory." In Undergraduate Texts in Mathematics, 257–82. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55193-3_14.

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Powell, Richard C. "Group Theory." In Symmetry, Group Theory, and the Physical Properties of Crystals, 25–53. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7598-0_2.

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Pommaret, J. F. "Group theory." In Partial Differential Equations and Group Theory, 177–258. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-2539-2_6.

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Hamermesh, M. "Group Theory." In Mathematical Tools for Physicists, 189–212. Weinheim, FRG: Wiley-VCH Verlag GmbH & Co. KGaA, 2006. http://dx.doi.org/10.1002/3527607773.ch7.

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Hassani, Sadri. "Group Theory." In Mathematical Physics, 651–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-87429-1_24.

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Stillwell, John. "Group Theory." In Undergraduate Texts in Mathematics, 361–81. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4684-9281-1_19.

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Smith, Geoff. "Group Theory." In Springer Undergraduate Mathematics Series, 125–52. London: Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-0619-7_5.

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Stillwell, John. "Group Theory." In Undergraduate Texts in Mathematics, 383–413. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6053-5_19.

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Conference papers on the topic "Group theory"

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Sehgal, Surinder, and Ronald Solomon. "Group Theory." In Biennial Ohio State – Denison Conference. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814535724.

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Stephens, C. R. "Renormalization Group Theory." In PARTICLES AND FIELDS: X Mexican Workshop on Particles and Fields. AIP, 2006. http://dx.doi.org/10.1063/1.2359403.

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Kugo, Taichiro. "Complex Group Gauge Theory." In Proceedings of CST-MISC Joint Symposium on Particle Physics — from Spacetime Dynamics to Phenomenology —. Journal of the Physical Society of Japan, 2015. http://dx.doi.org/10.7566/jpscp.7.010003.

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Baartman, Richard. "Summary: Theory working group." In Workshop on space charge physics in high intensity hadron rings. American Institute of Physics, 1998. http://dx.doi.org/10.1063/1.56779.

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Chacón, Elpidio. "Introduction to group theory." In The XXX Latin American school of physics ELAF: Group theory and its applications. AIP, 1996. http://dx.doi.org/10.1063/1.50216.

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Zhiqiang Feng. "Theory of group enterprise strategy." In 2012 First National Conference for Engineering Sciences (FNCES). IEEE, 2012. http://dx.doi.org/10.1109/nces.2012.6543836.

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Wang, Li-Tien, and Peter J. Angeline. "Evolutionary algorithm in group theory." In AeroSense 2002, edited by Kevin L. Priddy, Paul E. Keller, and Peter J. Angeline. SPIE, 2002. http://dx.doi.org/10.1117/12.458719.

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SUDARSHAN, E. C. G. "GROUP THEORY OF DYNAMICAL MAPS." In Quantum Information and Computing. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774491_0026.

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Vitale, Patrizia. "Aspects of group field theory." In XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. AIP, 2012. http://dx.doi.org/10.1063/1.4733364.

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Choubey, Sandhya, Thomas Schwetz, Chris Walter, Daniel Kaplan, Maury Goodman, and Zack Sullivan. "Working Group I Report (Theory)." In NEUTRINO FACTORIES, SUPERBEAMS, AND BETA BEAMS: 11th International Workshop on Neutrino Factories, Superbeams and Beta Beams—NuFact09. AIP, 2010. http://dx.doi.org/10.1063/1.3399397.

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Reports on the topic "Group theory"

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Keane, Michael K., and David W. Jensen. Computer Programming and Group Theory. Fort Belvoir, VA: Defense Technical Information Center, May 1990. http://dx.doi.org/10.21236/ada225155.

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Cho, Yong Seung. Finite Group Actions in Seiberg–Witten Theory. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-135-143.

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Goldin, Gerald A., and David H. Sharp. Diffeomorphism Group Representations in Relativistic Quantum Field Theory. Office of Scientific and Technical Information (OSTI), December 2017. http://dx.doi.org/10.2172/1415360.

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Chevassut, Olivier. Authenticated group Diffie-Hellman key exchange: theory and practice. Office of Scientific and Technical Information (OSTI), October 2002. http://dx.doi.org/10.2172/805133.

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Melhuish, Kathleen. The Design and Validation of a Group Theory Concept Inventory. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.2487.

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Birdsall, C. K. Plasma Theory and Simulation Group Annual Progress Report for 1989. Fort Belvoir, VA: Defense Technical Information Center, December 1989. http://dx.doi.org/10.21236/ada231967.

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Birdsall, Charles K. Plasma Theory and Simulation Group Annual Progress Report, for 1990. Fort Belvoir, VA: Defense Technical Information Center, December 1990. http://dx.doi.org/10.21236/ada233037.

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Starkman, Glenn David, and Harsh Mathur. Particle Astrophysics Theory Group, CWRU 2013 Final Report on DOE grant. Office of Scientific and Technical Information (OSTI), July 2013. http://dx.doi.org/10.2172/1087735.

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Birdsall, C. K. Plasma Theory and Simulation Group Third and Fourth Quarter Progress Report. Fort Belvoir, VA: Defense Technical Information Center, December 1988. http://dx.doi.org/10.21236/ada231284.

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Rahnema, Farzad, Alireza Haghighat, and Abderrafi Ougouag. Consistent Multigroup Theory Enabling Accurate Course-Group Simulation of Gen IV Reactors. Office of Scientific and Technical Information (OSTI), November 2013. http://dx.doi.org/10.2172/1111137.

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